ABSTRACT

The threshold dividend strategy, under which dividends are paid only when the insurer's surplus exceeds a pre-determined threshold, has received considerable attention in risk theory. However, in practice, it seems rather unlikely that an insurer will immediately pull back the dividend payments as soon as its surplus level drops below the dividend threshold. Hence, in this paper, we propose a refracted Lévy risk model with delayed dividend pullbacks triggered by a certain Poissonian observation scheme. Leveraging the extensive literature on fluctuation identities for spectrally negative Lévy processes, we obtain explicit expressions for two-sided exit identities of the proposed insurance risk process. Also, penalties are incorporated into the analysis of dividend payouts as a mechanism to penalize for the volatility of the dividend policy and account for an investor's typical preference for more stable cash flows. An explicit expression for the expected (discounted) dividend payouts net of penalties is derived. The criterion for the optimal threshold level that maximizes the expected dividend payouts is also discussed. Finally, several numerical examples are considered to assess the impact of dividend delays on ruin-related quantities. We numerically show that dividend strategies with more steady dividend payouts can be preferred (over the well-known threshold dividend strategy) when penalty fee become too onerous.

摘要

阈值红利策略是指只有当保险公司的盈余超过预定阈值时才支付红利的策略，在风险理论中受到了相当多的关注。然而，在实践中，一旦保险公司的盈余水平低于股息阈值，保险公司似乎不太可能立即撤回股息支付。因此，在本文中，我们提出了一种折射 Lévy 风险模型，该模型具有由某种泊松观察方案触发的延迟股息回调。利用关于谱负 Lévy 过程波动恒等式的大量文献，我们获得了所提出的保险风险过程的双边退出恒等式的显式表达式。还，惩罚措施被纳入股息支付分析中，作为惩罚股息政策波动的机制，并考虑到投资者对更稳定现金流的典型偏好。得出扣除罚金后的预期（贴现）股息支付的明确表达式。还讨论了最大化预期股息支付的最佳阈值水平的标准。最后，考虑了几个数值例子来评估股息延迟对破产相关数量的影响。我们通过数字表明，当罚款费用变得过于繁重时，可以优先选择具有更稳定股息支付的股息策略（相对于众所周知的阈值股息策略）。得出扣除罚金后的预期（贴现）股息支付的明确表达式。还讨论了最大化预期股息支付的最佳阈值水平的标准。最后，考虑了几个数值例子来评估股息延迟对破产相关数量的影响。我们通过数字表明，当罚款费用变得过于繁重时，可以优先选择具有更稳定股息支付的股息策略（相对于众所周知的阈值股息策略）。得出扣除罚金后的预期（贴现）股息支付的明确表达式。还讨论了最大化预期股息支付的最佳阈值水平的标准。最后，考虑了几个数值例子来评估股息延迟对破产相关数量的影响。我们通过数字表明，当罚款费用变得过于繁重时，可以优先选择具有更稳定股息支付的股息策略（相对于众所周知的阈值股息策略）。